Tagged Choice Counts and Actual Branch Widths

(0, [])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (0, []).

(0, [0])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (0, [0]).

(1, [1])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (1, [1]).

(6, [2, 2, 5, 6])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (6, [2, 2, 5, 6]).

(2, [1, 2])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (2, [1, 2]).

(3, [1, 3])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (3, [1, 3]).

(4, [1, 4])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (4, [1, 4]).

(5, [1, 5])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (5, [1, 5]).

(6, [1, 6])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (6, [1, 6]).

(7, [1, 7])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (7, [1, 7]).

(8, [1, 8])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (8, [1, 8]).

(9, [1, 9])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (9, [1, 9]).

(3, [2, 3])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (3, [2, 3]).

(4, [2, 4])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (4, [2, 4]).

(5, [2, 5])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (5, [2, 5]).

(6, [2, 6])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (6, [2, 6]).

(7, [2, 7])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (7, [2, 7]).

(8, [2, 8])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (8, [2, 8]).

(9, [2, 9])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (9, [2, 9]).

(10, [2, 10])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (10, [2, 10]).

(4, [3, 4])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (4, [3, 4]).

(5, [3, 5])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (5, [3, 5]).

(6, [3, 6])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (6, [3, 6]).

(7, [3, 7])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (7, [3, 7]).

(8, [3, 8])

Add category sizes in order; no categories give total zero. This is a choice protocol, not a probability-independence assumption. The exact result, retaining the requested order, is (8, [3, 8]).

(1, [])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (1, []).

(0, [0])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (0, [0]).

(0, [2, 0, 0])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (0, [2, 0, 0]).

(0, [0, 0, 0])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (0, [0, 0, 0]).

(0, [2, 6, 0, 0])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (0, [2, 6, 0, 0]).

(1, [1, 1])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (1, [1, 1]).

(2, [1, 2])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (2, [1, 2]).

(3, [1, 3])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (3, [1, 3]).

(4, [1, 4])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (4, [1, 4]).

(5, [1, 5])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (5, [1, 5]).

(6, [1, 6])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (6, [1, 6]).

(7, [1, 7])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (7, [1, 7]).

(8, [1, 8])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (8, [1, 8]).

(2, [2, 2])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (2, [2, 2]).

(4, [2, 4])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (4, [2, 4]).

(6, [2, 6])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (6, [2, 6]).

(8, [2, 8])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (8, [2, 8]).

(10, [2, 10])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (10, [2, 10]).

(12, [2, 12])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (12, [2, 12]).

(14, [2, 14])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (14, [2, 14]).

(16, [2, 16])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (16, [2, 16]).

(3, [3, 3])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (3, [3, 3]).

(6, [3, 6])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (6, [3, 6]).

(9, [3, 9])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (9, [3, 9]).

(12, [3, 12])

Multiply successive choice counts; an empty product is one and a zero stage makes later products zero. No stochastic independence is asserted. The exact result, retaining the requested order, is (12, [3, 12]).

(0, 0, Yes, 0)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (0, 0, Yes, 0).

(4, 4, No, 0)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (4, 4, No, 0).

(4, 4, Yes, 0)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (4, 4, Yes, 0).

(0, 0, Yes, 0)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (0, 0, Yes, 0).

(3, 2, No, -1)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (3, 2, No, -1).

(11, 0, No, -11)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (11, 0, No, -11).

(13, 0, No, -13)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (13, 0, No, -13).

(15, 0, No, -15)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (15, 0, No, -15).

(8, 0, No, -8)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (8, 0, No, -8).

(1, 2, No, 1)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (1, 2, No, 1).

(3, 2, No, -1)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (3, 2, No, -1).

(5, 2, No, -3)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (5, 2, No, -3).

(7, 2, No, -5)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (7, 2, No, -5).

(9, 2, No, -7)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (9, 2, No, -7).

(11, 2, No, -9)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (11, 2, No, -9).

(13, 2, No, -11)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (13, 2, No, -11).

(15, 2, No, -13)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (15, 2, No, -13).

(8, 2, No, -6)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (8, 2, No, -6).

(1, 4, No, 3)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (1, 4, No, 3).

(3, 4, No, 1)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (3, 4, No, 1).

(5, 4, No, -1)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (5, 4, No, -1).

(7, 4, No, -3)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (7, 4, No, -3).

(9, 4, No, -5)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (9, 4, No, -5).

(11, 4, No, -7)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (11, 4, No, -7).

(13, 4, No, -9)

Sum actual branches and check every width separately; equal totals do not establish equal widths. For no first-stage branches the width condition is vacuously Yes. The exact result, retaining the requested order, is (13, 4, No, -9).

(0, 0, 0)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (0, 0, 0).

(2, 1, 1)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (2, 1, 1).

(1, 1, 0)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (1, 1, 0).

(4, 2, 2)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (4, 2, 2).

(3, 2, 1)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (3, 2, 1).

(2, 2, 0)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (2, 2, 0).

(2, 2, 0)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (2, 2, 0).

(6, 3, 3)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (6, 3, 3).

(5, 3, 2)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (5, 3, 2).

(4, 3, 1)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (4, 3, 1).

(3, 3, 0)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (3, 3, 0).

(4, 3, 1)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (4, 3, 1).

(3, 3, 0)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (3, 3, 0).

(8, 4, 4)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (8, 4, 4).

(7, 4, 3)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (7, 4, 3).

(6, 4, 2)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (6, 4, 2).

(5, 4, 1)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (5, 4, 1).

(4, 4, 0)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (4, 4, 0).

(6, 4, 2)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (6, 4, 2).

(5, 4, 1)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (5, 4, 1).

(4, 4, 0)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (4, 4, 0).

(4, 4, 0)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (4, 4, 0).

(10, 5, 5)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (10, 5, 5).

(9, 5, 4)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (9, 5, 4).

(8, 5, 3)

Enumerate actual union/intersection membership; adding both cardinalities double-counts shared choices. No probability-independence premise is involved. The exact result, retaining the requested order, is (8, 5, 3).